Muutke küpsiste eelistusi

E-raamat: Linear Programming and Resource Allocation Modeling [Wiley Online]

(University of Hartford)
  • Formaat: 448 pages
  • Ilmumisaeg: 14-Dec-2018
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119509475
  • ISBN-13: 9781119509479
Teised raamatud teemal:
  • Wiley Online
  • Hind: 126,88 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Linear Programming and Resource Allocation ModelingSuurem pilt
  • Formaat: 448 pages
  • Ilmumisaeg: 14-Dec-2018
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119509475
  • ISBN-13: 9781119509479
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119509479

Guides in the application of linear programming to firm decision making, with the goal of giving decision-makers a better understanding of methods at their disposal

Useful as a main resource or as a supplement in an economics or management science course, this comprehensive book addresses the deficiencies of other texts when it comes to covering linear programming theory—especially where data envelopment analysis (DEA) is concerned—and provides the foundation for the development of DEA.

Linear Programming and Resource Allocation Modeling begins by introducing primal and dual problems via an optimum product mix problem, and reviews the rudiments of vector and matrix operations. It then goes on to cover: the canonical and standard forms of a linear programming problem; the computational aspects of linear programming; variations of the standard simplex theme; duality theory; single- and multiple- process production functions; sensitivity analysis of the optimal solution; structural changes; and parametric programming. The primal and dual problems are then reformulated and re-examined in the context of Lagrangian saddle points, and a host of duality and complementary slackness theorems are offered. The book also covers primal and dual quadratic programs, the complementary pivot method, primal and dual linear fractional functional programs, and (matrix) game theory solutions via linear programming, and data envelopment analysis (DEA). This book:

  • Appeals to those wishing to solve linear optimization problems in areas such as economics, business administration and management, agriculture and energy, strategic planning, public decision making, and health care
  • Fills the need for a linear programming applications component in a management science or economics course
  • Provides a complete treatment of linear programming as applied to activity selection and usage
  • Contains many detailed example problems as well as textual and graphical explanations

Linear Programming and Resource Allocation Modeling is an excellent resource for professionals looking to solve linear optimization problems, and advanced undergraduate to beginning graduate level management science or economics students.

Preface xi
Symbols and Abbreviations xv
1 Introduction
1(12)
2 Mathematical Foundations
13(22)
2.1 Matrix Algebra
13(7)
2.2 Vector Algebra
20(2)
2.3 Simultaneous Linear Equation Systems
22(4)
2.4 Linear Dependence
26(3)
2.5 Convex Sets and n-Dimensional Geometry
29(6)
3 Introduction to Linear Programming
35(8)
3.1 Canonical and Standard Forms
35(2)
3.2 A Graphical Solution to the Linear Programming Problem
37(1)
3.3 Properties of the Feasible Region
38(1)
3.4 Existence and Location of Optimal Solutions
38(1)
3.5 Basic Feasible and Extreme Point Solutions
39(2)
3.6 Solutions and Requirement Spaces
41(2)
4 Computational Aspects of Linear Programming
43(28)
4.1 The Simplex Method
43(5)
4.2 Improving a Basic Feasible Solution
48(18)
4.3 Degenerate Basic Feasible Solutions
66(3)
4.4 Summary of the Simplex Method
69(2)
5 Variations of the Standard Simplex Routine
71(24)
5.1 The M-Penalty Method
71(7)
5.2 Inconsistency and Redundancy
78(7)
5.3 Minimization of the Objective Function
85(1)
5.4 Unrestricted Variables
86(1)
5.5 The Two-Phase Method
87(8)
6 Duality Theory
95(28)
6.1 The Symmetric Dual
95(2)
6.2 Unsymmetric Duals
97(3)
6.3 Duality Theorems
100(6)
6.4 Constructing the Dual Solution
106(7)
6.5 Dual Simplex Method
113(1)
6.6 Computational Aspects of the Dual Simplex Method
114(7)
6.7 Summary of the Dual Simplex Method
121(2)
7 Linear Programming and the Theory of the Firm
123(72)
7.1 The Technology of the Firm
123(2)
7.2 The Single-Process Production Function
125(4)
7.3 The Multiactivity Production Function
129(10)
7.4 The Single-Activity Profit Maximization Model
139(4)
7.5 The Multiactivity Profit Maximization Model
143(3)
7.6 Profit Indifference Curves
146(2)
7.7 Activity Levels Interpreted as Individual Product Levels
148(7)
7.8 The Simplex Method as an Internal Resource Allocation Process
155(2)
7.9 The Dual Simplex Method as an Internalized Resource Allocation Process
157(1)
7.10 A Generalized Multiactivity Profit-Maximization Model
157(4)
7.11 Factor Learning and the Optimum Product-Mix Model
161(4)
7.12 Joint Production Processes
165(2)
7.13 The Single-Process Product Transformation Function
167(4)
7.14 The Multiactivity Joint-Production Model
171(9)
7.15 Joint Production and Cost Minimization
180(4)
7.16 Cost Indifference Curves
184(2)
7.17 Activity Levels Interpreted as Individual Resource Levels
186(9)
8 Sensitivity Analysis
195(22)
8.1 Introduction
195(1)
8.2 Sensitivity Analysis
195(14)
8.2.1 Changing an Objective Function Coefficient
196(4)
8.2.2 Changing a Component of the Requirements Vector
200(2)
8.2.3 Changing a Component of the Coefficient Matrix
202(7)
8.3 Summary of Sensitivity Effects
209(8)
9 Analyzing Structural Changes
217(10)
9.1 Introduction
217(1)
9.2 Addition of a New Variable
217(2)
9.3 Addition of a New Structural Constraint
219(4)
9.4 Deletion of a Variable
223(1)
9.5 Deletion of a Structural Constraint
223(4)
10 Parametric Programming
227(30)
10.1 Introduction
227(1)
10.2 Parametric Analysis
227(29)
10.2.1 Parametrizing the Objective Function
228(8)
10.2.2 Parametrizing the Requirements Vector
236(9)
10.2.3 Parametrizing an Activity Vector
245(11)
10.A Updating the Basis Inverse
256(1)
11 Parametric Programming and the Theory of the Firm
257(40)
11.1 The Supply Function for the Output of an Activity (or for an Individual Product)
257(5)
11.2 The Demand Function for a Variable Input
262(7)
11.3 The Marginal (Net) Revenue Productivity Function for an Input
269(7)
11.4 The Marginal Cost Function for an Activity (or Individual Product)
276(8)
11.5 Minimizing the Cost of Producing a Given Output
284(2)
11.6 Determination of Marginal Productivity, Average Productivity, Marginal Cost, and Average Cost Functions
286(11)
12 Duality Revisited
297(24)
12.1 Introduction
297(1)
12.2 A Reformulation of the Primal and Dual Problems
297(14)
12.3 Lagrangian Saddle Points
311(4)
12.4 Duality and Complementary Slackness Theorems
315(6)
13 Simplex-Based Methods of Optimization
321(52)
13.1 Introduction
321(1)
13.2 Quadratic Programming
321(4)
13.3 Dual Quadratic Programs
325(4)
13.4 Complementary Pivot Method
329(6)
13.5 Quadratic Programming and Activity Analysis
335(3)
13.6 Linear Fractional Functional Programming
338(9)
13.7 Duality in Linear Fractional Functional Programming
347(6)
13.8 Resource Allocation with a Fractional Objective
353(3)
13.9 Game Theory and Linear Programming
356(7)
13.9.1 Introduction
356(1)
13.9.2 Matrix Games
357(4)
13.9.3 Transformation of a Matrix Game to a Linear Program
361(2)
13.A Quadratic Forms
363(10)
13.A.1 General Structure
363(3)
13.A.2 Symmetric Quadratic Forms
366(1)
13.A.3 Classification of Quadratic Forms
367(1)
13.A.4 Necessary Conditions for the Definiteness and Semi-Definiteness of Quadratic Forms
368(1)
13.A.5 Necessary and Sufficient Conditions for the Definiteness and Semi-Definiteness of Quadratic Forms
369(4)
14 Data Envelopment Analysis (DEA)
373(32)
14.1 Introduction
373(1)
14.2 Set Theoretic Representation of a Production Technology
374(3)
14.3 Output and Input Distance Functions
377(2)
14.4 Technical and Allocative Efficiency
379(6)
14.4.1 Measuring Technical Efficiency
379(3)
14.4.2 Allocative, Cost, and Revenue Efficiency
382(3)
14.5 Data Envelopment Analysis (DEA) Modeling
385(1)
14.6 The Production Correspondence
386(1)
14.7 Input-Oriented DEA Model under CRS
387(3)
14.8 Input and Output Slack Variables
390(8)
14.9 Modeling VRS
398(4)
14.9.1 The Basic BCC (1984) DEA Model
398(2)
14.9.2 Solving the BCC (1984) Model
400(1)
14.9.3 BCC (1984) Returns to Scale
401(1)
14.10 Output-Oriented DEA Models
402(3)
References and Suggested Reading 405(6)
Index 411
Michael J. Panik, PhD, is Professor Emeritus in the Department of Economics at the University of Hartford, CT. He has taught courses in economic and business statistics, quantitative decision methods, introductory and advanced quantitative methods, and econometrics. Dr. Panik is the author of several books, including Stochastic Differential Equations and Growth Curve Modeling: Theory and Applications, both published by Wiley. He is also a co-author of Introduction to Quantitative Methods in Business: With Applications Using Microsoft Office Excel.
Püsilink: https://www.kriso.ee/db/9781119509479_pe.html
Märksõnad: